Heat a circulating water bath (or a saucepan filled with water) to 62.5°C (145°F). Add the eggs and cook for 1 hour. Remove the eggs from the water bath and leave to cool at room temperature.
Gently warm the clarified butter in a saucepan to 45°C (115°F). Crack the eggs and remove the egg yolks without breaking them. Place the egg yolks in the clarified butter and maintain the temperatu